A hybrid vehicle is capable of operating in an EV propulsion mode in which it travels in the state with its engine stopped. An engine startup system is per se known (refer to Patent Document #1) in which, when a request for starting the engine is issued during the EV propulsion mode, the engine is started by transmitting the torque of the electric motor to the engine via a clutch, and temporarily in this starting process the clutch is disengaged or its engagement force is reduced; and then, when the starting of the engine has been completed and after the difference between the input and output rotational speeds of the clutch has disappeared, the clutch is engaged so that the propulsion mode is changed over. Moreover, Patent Documents #2-#4 mentioned below in the Citation List are relevant to the present invention.